"In general the Greeks looked upon an axiom as something which was so self-evident that no reasonable person would object... while a postulate was a request that something be allowed. Now Euclid's fifth postulate... whatever else this postulate may be, self-evident it is not, and this was early perceived. ... The first line of attack was, naturally, the attempt to prove this postulate by the aid of others, and the axioms. Such, presumably, was Ptolemy's idea. But even if we grant that all of Euclid's axioms are self-evident, it does not... follow that he puts in his list all of the assumptions that he really uses."